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Geometry PAP Fall Final Review, Part 2 True/False 1. If two sides and a non-included angle of one triangle are congruent to two sides and a nonincluded angle of another triangle, then the triangles are congruent. 2. Given two angles and an included side, you can construct exactly one triangle. 3. A triangle with side lengths of 17, 63, and 65 would be obtuse. 4. All the points on a perpendicular bisector of a segment are equidistant to the endpoints of the segment. 5. It is possible to create a triangle with side lengths 12 cm, 7 cm, and 5 cm. 6. If a conditional statement is true, then its contrapositive is also true. 7. A diagonal of a square divides it into two equilateral triangles. 8. The altitude of an equilateral triangle is half a side length times the square root of 3. 9. An angle bisector of a triangle divides the opposite side into two segments that are proportional to the sides of the angle being bisected. 10. An exterior angle of a triangle is supplementary to the two remote interior angles. Fill in the Blank 11. A pentagon has ___________ diagonals. An n-gon has __________ diagonals. 12. If one of the base angles of an isosceles triangle has measure 40 degrees, then the vertex angle has measure _________. 13. In triangle ABC, if the measure of angle A is 50 degrees, and the measure of angle B is 72 degrees and the measure of angle C is 58 degrees, then ________ is the longest side. 14. Consider the statement: “If Alabama beats Notre Dame, they will be the national champions.” Write the converse, inverse and contrapositive. Which, if any, would be true? 15. Given the following figure: D Name all of the triangles with the given description: 16. a) scalene b) isosceles c) acute d) obtuse e) equilateral G E F The figure below was constructed such that line AB is parallel to line DE and C is the midpoint of segment AE. Are the two triangles created congruent? If so, name the congruent triangles and tell the reason they are congruent. B E C A D 17. Find the midpoint of the segment with endpoints (-1,-6) and (-15,8). 18. Find the value of y in terms of x: y x+15 22 19. (3,-5) is the center of a circle. If (7,3) is one endpoint of a diameter, what are the coordinates of the other endpoint? 20. If 2x and 3x are the two acute angles of a right triangle, what is the actual measurement of the angles? 21. Write a definition of: Supplementary angles – Linear pair – Skew lines – Diagonal of a polygon – 22. If triangle RPQ is congruent to triangle JKL, then segment LJ is congruent to __________. 23. If angle IJK is congruent to angle FHP, which, if any, lines must be parallel? K I J L M N G H P F Q 24. Given points H(-1,5) and K(7,1), find HK. O